<p style='text-indent:20px;'>In this paper, the modelling and analysis of prey-predator model involving predation of mature prey is done using DDE. Equilibrium points are calculated and stability analysis is performed about non-zero equilibrium point. Delay parameter destabilizes the system and triggers asymptotic stability when value of delay parameter is below the critical point. Hopf bifurcation is observed when the value of delay parameter crosses the critical point. Sensitivity analysis has also been performed to look into the effect of other parameters on the state variables. The numerical results are substantiated using MATLAB.</p>
A mathematical model is proposed to study the effect of toxin producing prey on predator population using delay differential equations. The associated state variables are Prey populations and predator populations. The assumption is that the toxicity released by prey population adversely affects the predator population. The feasible interior equilibrium is calculated. Hopf bifurcation is observed about the critical value of delay parameter. Analytical findings are supported using MATLAB simulation.
Chest pain is one of the common complaints encountered in clinical practice. Multiple diseases present as chest pain and often the etiology can be challenging to diagnose. Among the cardiac causes, coronary artery dissection is one of the life-threatening conditions and is often misdiagnosed as an acute coronary syndrome because of its similar presentation. In this case report, we will share a case of coronary artery dissection, which was initially managed as a non-ST-elevation myocardial infarction. We will share the modalities used to diagnose spontaneous coronary artery dissection and how the management differs between acute coronary syndrome and spontaneous coronary artery dissection.
In nature, many species form teams and move in herds from one place to another. This helps them in reducing the risk of predation. Time delay caused by the age structure, maturation period, and feeding time is a major factor in real-time prey–predator dynamics that result in periodic solutions and the bifurcation phenomenon. This study analysed the behaviour of teamed-up prey populations against predation by using a mathematical model. The following variables were considered: the prey population Pr1, the prey population Pr2, and the predator population Pr3. The interior equilibrium point was calculated. A local satiability analysis was performed to ensure a feasible interior equilibrium. The effect of the delay parameter on the dynamics was examined. A Hopf bifurcation was noted when the delay parameter crossed the critical value. Direction analysis was performed using the centre manifold theorem. The graphs of analytical results were plotted using MATLAB.
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